The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  X  1  1  1  1  1  0  1  X
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1  0 X+1  1  X X+1  1  1  0  0 X+1  0 X+1  1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  0  X  X  X  X  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  0  X  X  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  X  0  0  X  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  0  0  X  0  X  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  0  X  0  X  X  0  X  X  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  X  0  X  X  X  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  0  X  X  0  0  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  0  0  X  X  0  0  X  0  X  X  0  0  0

generates a code of length 30 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+172x^20+92x^22+644x^24+672x^26+1678x^28+1528x^30+1855x^32+704x^34+632x^36+76x^38+120x^40+14x^44+4x^48

The gray image is a linear code over GF(2) with n=60, k=13 and d=20.
This code was found by Heurico 1.16 in 3 seconds.